I don't think you understand the terminology. He has legitimate claim to be voted in because he defeated the High King in combat. That's the Old Way. The Empire conveniently forgets the past, but the North Remembers.
Old ways? Don't talk to me about old ways, ignorant mortal. Ask my lord Alduin if the "old ways' matter. Yes, the true ancient Nord ways, the Dragon Cult can educate you on that.